Shape measurement is a general term that includes sensing a structure's position in three dimensional space. This measurement coincides with what the human eye perceives as the position of an object. Since the eyes continually perform this task, one might assume that the measurement is simple. If one considers a length of rope, one can physically measure the position at every inch along the rope to estimate the shape. But this task is tedious and is increasingly difficult with more complex shapes. Another consideration is how to perform the measurement if the rope cannot be physically reached or seen. If the rope is contained within a sealed box, its position cannot be determined by conventional measurement techniques. The rope in this example can be replaced with an optical fiber.
Sensing the shape of a long and slender deformed cylinder, such as an optical fiber, is useful in many applications ranging for example, from manufacturing and construction to medicine and aerospace. In most of these applications, the shape sensing system must be able to accurately determine the position of the fiber, e.g., within less than one percent of its length, and in many cases, less than one tenth of one percent of its length. There are a number of approaches to the shape measurement problem, but none adequately addresses the requirements of most applications because they are too slow, do not approach the required accuracies, do not function in the presence of tight bends, or fail to adequately account for twist of the fiber. In many applications, the presence of torsional forces that twist the fiber undermine the accuracy, and thus, usefulness of these approaches.
Conventional approaches to measuring the shape of a fiber use strain as the fundamental measurement signal. Strain is a ratio of the change in length of a fiber segment post-stress verses the original length of that segment (pre-stress). As an object like a fiber is bent, material on the outside of the bend is elongated, while the material on the inside of the bend is compressed. Knowing these changes in local strain and knowing the original position of the object, an approximation of the new position of the fiber can be made.
In order to effectively sense position with high accuracy, several key factors must be addressed. First, for a strain-based approach, the strain measurements are preferably accurate to tens of nanostrain (10 parts per billion) levels. But high accuracy strain measurements are not readily attainable by conventional resistive or optical strain gauges. Therefore, a new technique to measure the strain to extremely high accuracy must be devised that is not strain-based in the conventional sense.
Second, the presence of twist in the optical fiber must be measured to a high degree of accuracy and accounted for in the shape computation. By creating a multi-core fiber that is helixed and has a central core, the twist of a fiber can be sensed. But the problem is how to obtain an accuracy of rotational position better than 1 degree. For a high accuracy rotational sensor, the position of strain sensors along the length of the fiber must also be known to a high degree of accuracy. Therefore, some way of measuring the rotation rate of the outer cores in the helixed fiber is desirable, which can then be used to correct the calculation of the fiber position.
Third, fiber with multiple cores that is helixed at a sufficient rate and with Bragg gratings (a conventional optical strain gauge) is difficult and expensive to make. It is therefore desirable to provide a method of achieving nanostrain resolutions without Bragg gratings.
Fourth, multi-core fiber is typically not polarization-maintaining, and so polarization effects are preferably considered.